* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture #3
Survey
Document related concepts
Casimir effect wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Potential energy wikipedia , lookup
Anti-gravity wikipedia , lookup
Circular dichroism wikipedia , lookup
Work (physics) wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Magnetic monopole wikipedia , lookup
Maxwell's equations wikipedia , lookup
Field (physics) wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Fundamental interaction wikipedia , lookup
Electromagnetism wikipedia , lookup
Lorentz force wikipedia , lookup
Transcript
Intermolecular Forces •“Review” of electrostatics -> today •Force, field, potentials, and energy •Dipoles and multipoles •Discussion of types of classical electrostatic interactions •Dr. Fetrow will do hydrogen bond and inclusion in force fields Electromagnetic force •One of the four fundamental forces of nature •Responsible for the vast majority of what we observe around us •The best-understood and best-tested of the forces of nature •Almost* all interactions we care about in biology come from electrons •Intermolecular forces can be divided into three types: •Direct charge interactions •Van der Waals interactions -> interactions between fluctuating charge distributions •Pauli interactions -> electrons don’t like to be onto of each other Coulomb’s Law •Like charges repel, unlike charges attract •Force is directly along a line joining the two charges q1 q2 r ke q1q2 Fe 2 r ke = 8.988109 Nm2/C2 -12 C2/ (N●m2) q1q2 = 8.85410 0 ˆ Fe r 2 4 0 r •This can change when not in vacuum Electric Fields •Electric Field is the ability to exert a force at a distance on a charge •It is defined as force on a test charge divided by the charge + + – –– + + + F Small test charge q E F /q Potential Energy of charges charge q •Suppose we have an electric field •If we move a charge within this field, work is being done •Electric Fields are doing work on Electric Field E the charge W F s qE s U W qE s q E s •If path is not a straight line, or electric field varies you can rewrite this as an integral U q E ds Electric Potential Point A •Path you choose does not matter. (conservative) B U q E ds A •Factor out the charge – then you have electric potential V Electric Field E Point B U V E ds q A B E F /q •Electric potential, and the electrostatic energy have the same relation as do the force and electric field Dipoles •A dipole is a postive and negative charge separated by a distance d •Commonly found in molecules! Though the distances and charges are much smaller! q2 = -1 C 10 cm Dipole moment is qd. It is a vector! 5 cm q1 = +1 C Why don’t the charge fly together? Electric Dipoles The electric dipole moment, p, of a pair of charges is the vector directed from –q to +q and has magnitude d*q + d If we place the dipole in an external field, then there is a torque on the dipole. q - + Each charge has a force of magnitude qE on it, and a lever arm of size d/2 . Electric Dipoles and torque q Fd sin q + - F=qE p The dipole rotates to increase the alignment Therefore, with the field. p=dq pE sin q So the torque vector is: ~ ~ ~ pE Electric Dipoles and Energy q + ~ ~ ~ pE - p Work is required to rotate the dipole against the field. So, dW dq pE sin qdq The work is transformed into potential energy, so Pick a convention for qi and,, q f U q pE sin qdq pE (cos q i i cos q f ) ~ ~ U pE cos q p E Multiple charges q3 r3 r1 q1 q2 r2 ke qi V ri We can handle multiple charges by considering each on explicitly, or by a multipole expansion Multipole expansion (qualitatively) When outside the charge distribution, consider a set of charges as being a decomposition of a monopole, a dipole { and higher order terms} The monopole term is the net charge at the center of the charges {often zero} The dipole moment has its positive head at the center of the positive changes, and its negative tail at the center of the negative charges Multipole expansion The multipole expansion expands a potential in a complete set of functions: Pi (cos q ) 4 0 i 0 r q i The significance is that we can study the different poles one by one, to understand any charge distribution Where might we have a significant dipole moment? Where might we have a significant quadrapole moment? Charge-Charge Interaction r q1q2 Ep 2 4 0 r 0 = 8.85410-12 C2/ (N●m2) When might we have charge-charge interactions?